代写EE 6615 Nanotechnology for Devices and Microsystems代写数据结构语言程序

EE 6615

Nanotechnology for Devices and Microsystems

Homework (5 questions, 100 points total)

Due October 18, 2024, at the beginning of Class (before 7:15 pm)

1. (20 points total)

Consider the diamond crystal structure shown below, with a lattice constant of a. Express your answers in terms of a.

a.   Calculate the atomic volume density (number of atoms per unit volume) of this crystal. (5 points)

b.   Using the labels shown in the Figure, write down which atoms correspond to the initial FCC lattice (without being shifted) and which atoms correspond to the shifted FCC structure. (5 points)

c.   Draw the <100> and <111> planes of this crystal (this should be 2-dimensional illustration with atoms label). Calculate the atomic area density (number of atoms per unit area) on the <100> and <111> planes. (10 points)

Fig. 1 Structure of diamond crystal.

2. (10 points total)

For Si crystal grown using Czochralski technique:

(a) Sketch the doping concentration of oxygen along the grown Si ingot (C(x)/Co vs. x with x =  0  at the top  and x =  1  at  the  bottom  of the  ingot)  assuming  the  initial  oxygen concentration is Co  and there is no doping concentration correction. (4 points)

(b) How to make the oxygen concentration in the grown Si ingot uniform from top to bottom and across the wafers? (6 points)

3. (30 points total)

Nikon Corporation announced the release of their cutting-edge NSR-S636E immersion scanner as shown in Fig. 2 (a) in January 2024, offering a high throughput of 280 wafers/hour, which is 10-15% higher than current models. NSR-S636E adopts ArF with a wavelength of 193 nm as light source. The system has a high NA of 1.35 and is immersed in pure water with a refractive index n = 1.44, and it offers a resolution of 35 nm.

(a) (i) What’s the k1 of the system? (ii) What’s the collection angle o of the system? (iii) What will the NA and resolution be if we use air instead of water as medium? Please explain the reason. (12 points)

(b) Fig. 2 (b) shows the structure we want to fabricate, which has a substrate with a length L3 of 800 μm, a bottom square structure with a length L2 of 400 μm, and top two square structures with  a gap d of 100  μm  and  lengths  L1   of 80  μm.  We  use  a negative photoresist to fabricate the first layer (bottom square) and a positive photoresist to do the second one (top two squares). Draw the two photomasks needed (no need to consider alignment marks). Please label the key dimensions on the masks. (6 points)

(c) For the second step of lithography – draw the cross-section of the photoresist along the dashed line in Fig. 2 (b) after development under normal exposure condition, over exposure condition, and under exposure condition. Please label the key dimensions (qualitatively, compared to normal exposure). (6 points)

(d) If d = 20 nm, draw the cross-section view of the fabricated structures under normal exposure condition. (6 points)

Fig. 2 (a) Schematic of immersion lithography system. (b) Perspective view (top) and top view (bottom) of the fabricated structure.

4. (20 points total)

An exposure dosage curve for a 1.5 µm thick positive photoresist is shown in Figure 3. Do (critical dose) is 1.2 mJ/cm2 and D1  (minimum dose) is 0.5 mJ/cm2.

a)    Calculate the photoresist contrast. (6 points)

b)    Calculate and draw the cross-section of the exposed and developed photoresist. Label all the dimensions (height, widths) for A and B. Calculate the angle of the developed photoresist profile for A and B. (14 points)

Figure 3. Exposure dose profile.

5.         (20 points total)

Using dry etching, photoresist (PR) is an etch mask and amorphous silicon (a-Si) will be etched by RIE as shown in Fig. 4.

(a) Suppose a step height between the photoresist coated and uncoated area is 400 nm and it becomes 700 nm after etching for 3 min. After photoresist stripping, the step is measured to be 600 nm. What are the photoresist and a-Si etch rates, and their etch selectivity? (6 points)

(b) Using the same etch rates as (a), now the photoresist = 800 nm, a-Si = 1000 nm, etching is completely anisotropic and etch time = 6 min. Draw the cross-section of the etched structure. Please clearly label your drawing with critical dimensions. (6 points)

(c) Using the same etch rates as (a) and the layers as in (b), now let the lateral etch rate of a-Si be the same as the vertical etch rate, which is isotropic etching. After isotropic RIE for 2 min, draw the cross section of the etched structures. Please clearly label all critical dimensions. (8 points)

Fig. 4 Cross-section of patterned photoresist (PR) etch mask on top of amorphous Si (a-Si) on SiO2 substrate.